The dynamics of many ecological systems are profoundly influenced
by spatial heterogeneity in consumers and resources. Many consumers
cope with environmental heterogeneity by using biased random
walks, i.e., behaviors that are stochastic but have statistical
biases that may lead to up-gradient movement over the long term.
In particular, these organisms have internal state dynamics,
in which internal state is affected by the environment and behavior
is in turn determined by internal state. Population distributions
that result from individual-level biased random walks can often
approximated by advection-diffusion equations (ADEs), in which
the diffusion and advection coefficients implicitly represent
the sensory, physiological, or cognitive responses underlying
the behavior. I will present some examples of biased random
walks from marine and terrestrial systems (including some preliminary
experimental results on zooplankton) and derive ADEs that may
approximate the corresponding population fluxes. I will also
present an extension of this theory that combines group fission/fusion
dynamics with spatial random walks to obtain ADEs with density-dependent
coefficients that describe how grouping behavior may alter population
movements.